73 citations · 1.5k across the 132 of their papers we have counts for
12 papers · 1 filter
Conservative algebras of -dimensional algebras, IV
Amir Fernández Ouaridi, Ivan Kaygorodov, Cándido Martín González
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensi…
Central extensions of axial algebras
Ivan Kaygorodov, Cándido Martín González, Pilar Páez-Guillán
In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial centra…
Transposed Poisson structures on Witt type algebras
Ivan Kaygorodov, Mykola Khrypchenko
We describe -derivations, and hence transposed Poisson algebra structures, on Witt type Lie algebras , where is non-trivial and . More…
Transposed Poisson structures on Galilean and solvable Lie algebras
Ivan Kaygorodov, Viktor Lopatkin, Zerui Zhang
Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal Galilean Lie algebras do not have non-trivial…
Transposed Poisson structures on Block Lie algebras and superalgebras
Ivan Kaygorodov, Mykola Khrypchenko
We describe transposed Poisson algebra structures on Block Lie algebras and Block Lie superalgebras , where is an arbitrary complex number. Speci…
Transposed Poisson structures
Patrícia Damas Beites, Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Fu…
The algebraic and geometric classification of Zinbiel algebras
María Alejandra Alvarez, Renato Fehlberg Júnior, Ivan Kaygorodov
This paper is devoted to the complete algebraic and geometric classification of complex -dimensional Zinbiel algebras. In particular, we proved that the variety of complex -d…
The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
María Alejandra Alvarez, Ivan Kaygorodov
This paper is devoted to the complete algebraic and geometric classification of complex -dimensional nilpotent weakly associative, complex -dimensional symmetric Leibniz alge…
Products of commutator ideals of some Lie-admissible algebras
Ivan Kaygorodov, Farukh Mashurov, Tran Giang Nam +1
In this article, we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More pre…
Symmetric Zinbiel superalgebras
Saïd Benayadi, Ivan Kaygorodov, Fahmi Mhamdi
The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index of a symmetric Zinbiel superalgebra is not greater than 4 and describe two-generated…
Local derivations of semisimple Leibniz algebras
Ivan Kaygorodov, Karimbergen Kudaybergenov, Inomjon Yuldashev
We prove that every local derivation on a complex semisimple finite-dimensional Leibniz algebra is a derivation.
On the Kantor product, II
Renato Fehlberg Júnior, Ivan Kaygorodov
We describe the Kantor square (and Kantor product) of multiplications, extending the classification proposed in [I. Kaygorodov, On the Kantor product, Journal of Algebra and Its Ap…